AbstractA new self-adaptive fusion algorithm based on DST andDSmTisproposed.Inthenewalgorithm,partofthe conflicting information is normalized according to DST, while the otherpartisprocessedbyDSmT.Acontrollingfactorisusedto controlthequantityofinformationdealtbythetwodifferent methodsadaptively,whichisanewmethodavoidingsettingfor thethresholdofconflict.Thesimulationresultsindicatethatthe new self-adaptive fusion algorithm based on DST and DSmT can dealwithanyconflictingsituationwithagoodperformanceof convergence. KeywordsDST;DSmT;controllingfactor;information fusion I.INTRODUCTION Duetothecomplexityofmodernbattlefield,target identificationisbecomingmoreandmorecomplex.Itis difficulttogiveanaccurateandcredibleidentifyingresult onlybyonesensor.Therefore,targetidentificationbasedon multi-sourceinformationisbecomingahottopic.Dempster-Shafertheory(DST)isanefficientmethodforuncertainty consequence([1]).Itiswidelyusedinthedomainof synthesizeidentification.However,DSTcantgiveefficient fusionresultswheninformationfromdifferentsources becomeshighlyconflict.Manyimprovementareproposed, suchasYagersruleofcombination([2]),Murphysruleof combination([3]),Dengyongsruleofcombination([4])etc. DezertpresentedtheDezert-Smarandachetheory(DSmT) ([5]), which can be considered as an extension of the classical DST.DSmTperformswellindealingwiththefusionof uncertain,highlyconflictingandimprecisesources.Itcan solvenotonlythestaticproblemsbutalsothecomplex dynamic fusion problems. DSTandDSmThavetheirownadvantagesand disadvantagesforfusingthemulti-sourceinformation.The advantagesofDSTmainlyoccurinthecaseoflowdegreeof conflict,whereasitmaygiveabadfusionresultwhichis absolutelycontrarytothefactwhilethesourcesareinhigh degree of conflict. DSmT is more efficient in combining highly conflictingsources,butitoffersconvergencetowardcertainty slowlyespeciallyinlowdegreeofconflict.Soanewself-adaptivefusion algorithm is put forward in this paper. II. REVIEW OF THE THEORY OF EVIDENCEA.DST DSTwasfirstlyproposedbyDempsterin1967and extended by Shafer. The main idea will be reviewed as follows. Let 1{ , , }n =betheframeofdiscernmentofthefusion problemandallelementsof areexclusive.Abasicbelief assignment (BBA): 2 [0,1] mis defined as 2( ) 1( ) 0AmAm ==(1) where2 is the power set of and it includes all its subsets . For two independent bodies of evidence whose BBAs are denotedby 1mand 2mrespectively,theBBAofthe combination of the two bodies is given by the following rule 1 2, 2 ,12( ) ( ), ,( )10,A B A B X m A m BX Xm XkX = = = (2) where 1 2( ) ( )A Bk m A m B == reflects the conflict degree of the two sources. B.DSmT DSmT,anextensionofDST,wasdevelopedbyDezert andSmarandanche([5]).DSmTdiffersfromDSTatthatthe elementsof couldbeoverlapped.Forsimplicity,useD (Hyper-powerset)todenotethesetofallcompositionsbuilt fromelementsofwithandoperators.The generalized basic belief assignment (GBBA) : [0,1] mDis defined as( ) 1( ) 0A DmAm == (3) Similarly,theclassicalcombinationrulefortwo independentbodiesofevidence,whoseGBBAsare 1mand 2mrespectively, is given by Originally published as Yu X.H., Zhou Q.-J., Li Y.-L., An J., Liu Z.-C., A new self-adaptive fusion algorithm based on DST and DSmT, in Proc. of 17th Int Conf on Information Fusion, Salamanca, Spain, July 7-10, 2014, and reprinted with permission.Xiao-Hong YuQing-Jun ZhouYan-Li Li Jin AnZhi-Cheng LiuA New Self-Adaptive Fusion AlgorithmBased on DST and DSmT Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 42311 2, ,( )( ) ( ), ,( )0,fA B D A B XMm A m B X D Xm XX = = = (4) ItisremarkedthatDSmTkeepstheconflictinginformation and doesnt need normalization. ThebiggestdifferencebetweenDSTandDSmTcanbe intuitivelydescribedasfollows.Let 1 2{ , } =betheframe of discernment (without any extra conditions). The DST deals withBBA( ) [0,1] m suchthat1 2 1 2( ) ( ) ( ) 1 m m m + + = , whiletheDSmTdealswithGBBA( ) [0,1] m such that1 2 1 2 1 2( ) ( ) ( ) ( ) 1 m m m m + + + = . C.Self-adaptive fusion algorithm based on DST and DSmT AlthoughDSTbehaveswellwhilefusingsourcesarein lowdegreeofconflict,itmaygiveafusionresultthat absolutelycontrarytothefactwhiletwosourcesareinhigh degreeofconflict.Luckily,DSmTiscapableoffusingthe highlyconflictingsources.Anaturalideacomesoutthata self-adaptive fusion algorithm based on DST and DSmT could beusedtoobtainbetterperformanceinawayofsimple combination,thatis,ifthedegreeofconflictislessthana giventhreshold,Dempster-Shafercombinationrulecanbe used, otherwise DSm combination rule will be selected. Thelimitationofapplyingtheaboveideainpracticeis that a threshold of conflict should be set in advance.It is very difficulttodetermineasuitablevaluefortheconflicting thresholdsincedifferentsystemshavedifferentdegreesof conflict,andanexperientialvalueisusuallyusedinsteadthe trueonebyexperimentingtimeaftertime.Theriskliesthat once the threshold is not suitable, fusion results will be bad.Tosolvetheaboveproblem,thispaperproposedanew self-adaptivealgorithmbasedonDSTandDSmT,which avoids setting for the conflicting threshold in advance.III. A NEW SELF-ADAPTIVE FUSION ALGORITHMNotethatthekeydifficultyliesinhowtoprocessthe conflictinginformation.Beforeintroducingthenewself-adaptivefusionalgorithm,wewillreviewtheexisting methods and explain why we adopt such an algorithm.AccordingtoDST,conflictingpiecesofinformation betweentwobodiesofevidenceareeliminatedbymaking normalization.Yager([2])distributedtheconflicting informationtotheunionofallelements,andviewedthe conflict as unreliable and ignored it. Smets ([8]) distributed the conflictinginformationtoemptyset.Hepointedoutthatall thesourcesofevidencearereliablebuttheframeof discernmentisnotcompleteandtheactualresultmaylieout oftheframe.ThelimitationofDSTmethodisthatitcannot deal with the cases of high degree conflicts. On the contrary, DSmT keeps the conflicting information usefulandredistributestheconflictinginformationaccording tosomeprincipleswhilefusing.Itiscapableofcopingwith thecasesofhighdegreeconflicts,butitoffersslow convergence for the result. ToabsorbtheadvantagesofDSTandDSmT,thenew algorithmwilltreattheconflictinginformationina combinationway,thatis,partoftheconflictinginformation will be distributed to the nonempty set averagely and the other willberedistributedbyotherprinciples.Acontrollingfactor will be proposed to decide the mass of conflicting information to be normalized or not. A.Evaluation of conflict between bodies of evidence Definition1(Conflict)[6].Aconflictbetweentwobeliefsin DStheorycanbeinterpretedqualitativelyasonesource stronglysupportsonehypothesisandtheotherstrongly supportsanotherhypothesis,andthetwohypothesesarenot compatible. It iswell known that, thekey problem of designingself-adaptive fusion algorithm based on DST and DSmT is how to compute the conflict between two bodies of evidence. Next we willshowthattheexistingmeasures,includingtheconflict coefficientusedinDSTandDSmTandthedegreeof similarity,arenotsuitabletoactasaeligiblemeasurefor conflictinginformation,althoughtheformerhaslongbeen taken as a fact in the DempsterShafer theory community. We also propose a new measure to fill in this gap. Example1.Letbeaframeofdiscernmentwithnhypotheses1{ , , }n .Assume 1mand 2maretwoBBAs offered by two distinct sources which are defined as 1( ) 1/im n = 2( ) 1/im n = 1, 2, , i n = Obviously, the two BBAs are totally consistent with each other.Sothereshouldntexistconflict.Firstly,computethe conflictcoefficientandget 1 1/ k n = ,wherenisthe numberofhypothesesinframeofdiscernment.Secondly,It canbefoundoutthatalongwiththeincreaseof n ,k will increaseandapproachto1,asshownintherelationship betweenkandnisshownasFig.1.Ifkistakenasa measurementofthedegreeofconflict,thetwobodiesof evidenceareinhighdegreeofconflictwhennislargerthan 5. It is surely contrary to the fact.Fig.1. Relationship betweenk andn in example 1 Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4232Example2.Letbeaframeofdiscernmentwithtwo hypotheses1 2{ , } .TheBBAsofferedbytwosourcesare defined as 1 1( ) m p = , 1 2( ) 1 m p = 2 1( ) 1 m p = , 2 2( ) m p =where [0,1] p .Itisobviousthatthetwobodiesof evidence are highly contradicted with each other. According to DST,theconflictcoefficientcanbecalculated as2 2(1 ) k p p = + .Fig2showstherelationshipbetween kand p . As p changes from 0 to 1, kwill decrease from 1 to0.5andthenincreaseto1again,asshowninFig2.Note thatkislowthan1atmosttimeespeciallywhilepis around 0.5. It cant reflect the conflict between two sources of evidence rightly. Fig.2. Relationship betweenk andn in example 2FromExample1and2,wecanseethattheconflict coefficientkcant be used as a suitable measure of conflict. Toovercometheaboveshortage,someotherevaluating methodsofconflictareputforward,suchasthedegreeof similarity.Sincethesimilarityoftwobodiesofevidencecan alsoreflecttheirconflict,itcanbeusedasacandidateto reveal the conflict between two sources of evidence. Generally speaking, the larger the degree of similarity is, the smaller the conflict is. Usually, the degree of similarity can be calculated by the distance between bodies of evidence. There are some kinds of distance being used in information fusion, such as the famous theEuclideandistance([7])proposedbyCuzzolin,the Bhattacharyyadistance([8])givenbyRisticandSmets.Both ofthemaredefinedintheframeofDempster-Shafertheory. Nevertheless,neitherofthemcanreflectthesimilarityofthe subset of frame . Besides, Tessem turned the belief function intotheprobabilityfunctionbypignistictransformationand evaluated the distance between bodies of evidence in the level ofpignistic([9]).However,thedistancedefinedinthisway doesntaccordwiththedistancetheory.Novaluabledistance canbeusedinpracticeuntilthecomingoutofJousselme distance([10]),whichisthemostwidelyuseddistanceof evidenceatpresent.ThedefinitionofJousselmedistanceis given as follows. Definition2(Jousselmedistance).Letbeaframeof discernmentwithnhypotheses.TheBBAsofferedbytwo sensorsaredenotedas 1mand2m .Distancebetweenthem can be defined as 1 2 1 2 1 21( , ) ( ) ( )2TDis mm m m D m m = (5) where ( )| || |i jiji jA BD DA B = = isa2 2n n -dimensional matrix,and| | AdenotesthenumberofelementsofA .It reflectsthedegreeofsimilarityoftheevidence.Formula(5) can be rewritten as2 21 2 1 2 1 21( , ) (|| || || || 2 , )2Dis mm m m mm = + < >where 2|| || ,i i im mm =< >,1, 2 i = , and2 21 2 1 21 1| |, ( ) ( )| |n ni ji ji ji jA Bmm m Am BA B= =< >=is the product of two vectors. NotethatintheframeofdiscernmentinDSmT, hypothesescouldbeoverlappedpotentially.Thena generalized Jousselme distance is defined as follows. Definition3(generalizedJousselmedistance).Let bea fameofdiscernmentinDSmTwithnhypothesis.Thetwo GBBAsofferedbysensorsaredenotedas 1mand2m . Distance between them is defined as1 2 1 2 1 21( , ) ( ) ( )2TDis mm m m D m m = (6) where ( )| || |i jiji jA BD DA B = = isaN N -dimensional matrix,Nis thenumber of elements in the power set of, and| | AdenotestheDSmcardinalityof A .Similarly, distance can be transformed as2 21 2 1 2 1 21( , ) (|| || || || 2 , )2Dis mm m m mm = + < > ,where 2|| || ,i i im mm =< >,1, 2 i = , and 1 2 1 21 1| |, ( ) ( )| |N Ni ji ji ji jA Bmm m Am BA B= =< >=,A D . Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4233Itiseasytoseethat1 2( , ) [0,1] Dis mm ,andthedegree of similarity can be defined as1 2 1 2( , ) 1 ( , ) Sim mm Dis mm = (7) Obviously, it has1 2( , ) [0,1] Sim mm . Inexample1,theJousselmedistanceisalways0no matterwhatthevalueofnbe.Inotherwords,thesimilarity betweentwobodiesofevidenceisalways1,itaccordswith thefact.Inexample2,theJousselmedistanceiscomputed as1 2( , ) | 1 2 | Dis mm p = .As p changesfrom0to1,the Jousselme distance decreases from 1 to 0 and then increases to 1 again. It is also reasonable in intuition. However, one cannot determinethevalueofconflictbetweentwobodiesof evidence correctly just by the similarity. We will show this by the following Example 3. Example3.Letbeaframeofdiscernmentwithtwo hypotheses 1 2{ , } .ThetwoBBAsofferedbysensorsare defined as 1 1( ) 0.8 m = , 1 1 2( ) 0.2 m = 2 1 2( ) 1 m = Simplecalculationwillyield1 2( , ) 0.5657 Dis mm = , and1 2( , ) 0.4343 Sim mm = .Iftheconflictisestimatedby thedegreeofsimilarity,thetwosourcesofevidencearein conflict.However,itisobviousthatthesecondbodyof evidenceistotallyunknown.Thusonecantassertthatthey areinconflict.Inotherwords,itisnotcredibletodetermine the degree of conflict only by on the degree of similarity. Insummary,neitherconflictcoefficientnordegreeof similaritycanbeusedasthequantitativemeasureofconflict alone. A natural idea comes out that one may make a judgment objectivelybyconsideringthetwofactorssynthetically. Actually,manyresearchersfollowedthisway.Forexample, Jiang([12])tooktheaverageofJousslemedistanceand conflictcoefficientasthenewmeasureforconflict.Liu([6]) madethedualisticarraybyconflictcoefficientandthe distance between betting commitments to analysis the conflict under different situations. Liu ([13]) used the geometric mean ofconflictcoefficientanddistancebetweenbetting commitments as the measure of the conflict. This paper also adopts the above idea. One will see in the followingtextthat,inournewcombinationmodelthereare two places where the degrees of conflict need to be estimated. Ononeside,theclassicalconflictcoefficientistakento measure the value of conflict. On the other side, the similarity betweenbodiesofevidenceisusedasacontrollingfactorto distribute the conflicting information. See next for details. B.New combination rule Let 1{ , , }n = beadiscernmentframewithnhypotheses.Thehypothesesoftheframecouldbenon-exclusive.D isthehyper-powerset.Thegeneralizedbasic belief assignment is defined as: [0,1] mDwhere ( ) 1( ) 0A DmAm == (8) Let 1mand 2mbetheGBBAsoftwosensorswhichare independent with each other. The new combination rule can be defined as 1 2,12 '( ) ( ) ( )( ) , ,1A B DA B Xm A m B PXm X X D Xk= += (9) where1 2, ,( ) ( )A B D A Bk m A m B == reflectsthemassof conflict, 'k k =istheconflictthatwillbedistributedtothe allhypothesesaveragelybynormalizing.Therest(1 )k willberedistributedbyotherrules.Hereisacontrolling factor.Denotetheconflictinginformationthatbedistributed to hypothesisXby ( ) PX , and thus ( ) (1 )X DPX k = . Itcanbeseenfromformula(9)that,as changes,the fusionresultswillbedifferent.When 0 = ,allconflict informationwillbekeptanddistributedtothehypotheses whichbringontheconflict,andthenthenewalgorithmwill degenerate to DSm combination rule. When 1 = , all conflict informationwillbedistributedtoallhypothesesaveragely, and then the new algorithm will degenerate to DS combination rule. When (0,1) , part of the conflict will be kept as useful andtherestwillbedistributedaveragely,thenthenew algorithm is the synthesis of DSm and DS combination rules. Thenewalgorithmusesthedegreeofsimilarityasthe controllingfactor to adjust the fusion result adaptively.Letsbethenumberofsources.If 2 s = ,then1 2( , ) Sim mm = ; if 2 s > , then min{ ( , ) | , 1, , }i jSim mm i j s = =. Whiletherearemorethantwosourcestobefused,the new combination rule can be defined as 1'( ) ( )( ) , ,1ij iA X j sm A PXmX X D Xk= += (10) where 'k k = , 1( )ij iA j sk m A = = . C.Conflict distribution rule Tocopywiththecomplexconstraintsinrealsystems, DezertproposedthehybridDSmcombinationrule,which worksproperlyevenifinhighdegreeofconflict.However, due to the big number of element in D, it cannot offer quick convergenceandcosttoomuchtimeforcalculation.To achieveabetterperformance,somenewdistributionrules basedontheDSmruleareputforwardandareclassifiedas PCR1~PCR6 accordingtodistributionrules([11]).Itis remarkedthatPCR5isthoughttobethemostprecisein distribution and its combination rule is defined as Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 42341 22 21 2 2 11 2 2 1( ) ( ) ( )( ) ( ) ( ) ( )( ) ( ) ( ) ( )A B XY DX YmX m A m Bm Xm Y m XmYm X m Y m X mY=== + + + + (11) where, X D X . AccordingtoPCR5,theconflictinginformationcaused byXandY willbedistributedtothemselveswithout considering of their union. In fact, the conflicting information isdecompoundedtotwopartsas 1 2( ) ( ) m Xm Yand2 1( ) ( ) m XmY ,whichwillbedistributedseparately. HypothesesXandY willgettheconflictinginformationin proportiontotheirbasicbeliefassignments.Duetothehigh performance,PCR5iswidelyusedinrealsystems.Asan upgradedversionofPCR5,PCR6isthelatestrulewhichis usedtofusemorebodiesofevidenceandhasalsobeen applied in real systems.OuralgorithmalsoadoptsthePCR5forconflict distribution,andthentheitem ( ) PXinformula(9)couldbe rewritten as: 2 21 2 2 11 2 2 1( ) ( ) ( ) ( )( ) (1 )( ) ( ) ( ) ( )Y DX Ym Xm Y m XmYPXm X m Y m X mY= = + + + (12) If there are more than two sources, they can be combined onebyoneaccordingtoPCR5.Inaddition,theycanalsobe combinedaccordingtoPCR6,andtheitem( ) PXinformula (9) could be rewritten as 1( )11( ) ( )1 211( ) ( )1( ) (1 )( )( )( ) ( )i iskii i ksj jsjisiY Xi j jjPXm Ym Xm X m Y ====== + (13) where ,( )1,ij j ijj j i< = + . D.Realization of the new algorithm Let 1{ , , }n = beaframeofdiscernmentwithn hypotheses. 1( )im Aand 2( )jm Barethebasicbelief functionsoftwosourceswhichareindependentwitheach other,where1( ) 1iiA Dm A=,2( ) 1jjB Dm B=.Thenewself-adaptivefusionalgorithmbasedonDSTandDSmTcanbe describedasfollowingfoursteps.Hereweuse( ) mXto denote the fusion result. Step1., X D X ,set( ) 0 mX =and 0 k = .Compute 1 2( , ) Dis mm,1 2( , ) Sim mm , and 1 2( , ) Sim mm = .Step2., 1, 2, i j =,compute1 2( ) ( )i jm Am B . Ifi jA B ,thenrenew( )i jmA B with 1 2( ) ( ) ( )i j i jmA B m Am B + ,elserenewk with 1 2( ) ( )i jk m Am B +,renew( )imAwith 21 2 1 2( ) (1 ) ( ) ( ) / ( ( ) ( ))i i j i jmA m Am B m A m B + + ,and renew ( )jmBwith 21 2 1 2( ) (1 ) ( ) ( ) / ( ( ) ( ))j i j i jmB m Am B m A m B + + ;Step3. If all of 1 2( ) ( )i jm Am Bhave been computed, go to step4; otherwise, go to step 2; Step4.X D ,if X = , ( ) 0 mX = ;otherwise, ( ) ( ) / (1 ) mX mX k = . IV. NUMERICAL EXAMPLESuppose five sensors are used to detect targets which are independentwitheachother.Let{ , , } A B C =betheframe of discernment. Elements in are exclusive. Example1(noconflictingevidence):Thebasicbelief assignments offered by five sensors are given as follows. Evidence 1: 1 1 1( ) 0.5, ( ) 0.2, ( ) 0.3 m A m B mC = = = ; Evidence 2: 2 2 2( ) 0.6, ( ) 0.2, ( ) 0.2 m A m B m C = = = ; Evidence 3: 3 3 3( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Evidence 4: 4 4 4( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Evidence 5: 5 5 5( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Itiseasytoseethatallbodiesofevidencesupportthe identityAandtheyareinlowdegreeofconflict.Fusion resultsofferedbydifferentcombinationrulesaregivenin table 1. Example2(oneconflictingbodyofevidence):Thebasic beliefassignmentsofferedbyfivesensorsaregivenas follows. Evidence 1: 1 1 1( ) 0.5, ( ) 0.2, ( ) 0.3 m A m B mC = = = ; Evidence 2: 2 2 2( ) 0, ( ) 0.9, ( ) 0.1 m A m B m C = = = ; Evidence 3: 3 3 3( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Evidence 4: 4 4 4( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Evidence 5: 5 5 5( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Itisobviouslythatmostbodiesofevidencesupportthe identityAbutthesecondbodyofevidencesupportsthe identity B. In other words, they are in high degree of conflict. Fusion results offered by different combination rules are given in table 2. Example3(twoconflictingbodiesofevidence):Thebasic beliefassignmentsofferedbyfivesensorsaregivenas follows. Evidence 1: 1 1 1( ) 0.5, ( ) 0.2, ( ) 0.3 m A m B mC = = = ; Evidence 2: 2 2 2( ) 0, ( ) 0.9, ( ) 0.1 m A m B m C = = = ; Evidence 3: 3 3 3( ) 0.3, ( ) 0.6, ( ) 0.1 m A m B m C = = = ; Evidence 4: 4 4 4( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Evidence 5: 5 5 5( ) 0.55, ( ) 0.1, ( ) 0.35 m A m B m C = = = ; Asinexample2,mostbodiesofevidencesupportthe identityA,buttherearetwobodiesofevidencesupportthe identityB.Theyarealsoinhighdegreeofconflict.Fusion Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4235resultsofferedbydifferentcombinationrulesaregivenintable 3. TABLE 1. FUSION RESULTS OF EXAMPLE 1 Fusion algorithm Element ofD1 2m m1 2 3m m m1 2 3 4m m m m1 2 3 4 5m m m m mDST A 0.75 0.8684 0.9213 0.9503B 0.1 0.0211 0.0041 0.0007C 0.15 0.1105 0.0746 0.049PCR5A 0.6529 0.7087 0.7373 0.7506B 0.1426 0.0602 0.0281 0.0201C 0.2045 0.2311 0.2346 0.2293New self-adaptive combination rule A 0.7289 0.8235 0.8598 0.8755B 0.1092 0.0303 0.0113 0.008C 0.1619 0.1462 0.1289 0.1165TABLE 2. FUSION RESULTS OF EXAMPLE 2 Fusion algorithm Element ofD1 2m m1 2 3m m m1 2 3 4m m m m1 2 3 4 5m m m m mDST A 0 0 0 0B 0.8571 0.6316 0.3288 0.1228C 0.1429 0.3684 0.6712 0.8772PCR5 A 0.2024 0.37 0.5101 0.6154B 0.6851 0.4482 0.258 0.1247C 0.1125 0.1818 0.2319 0.2599New self-adaptive combination rule A 0.1797 0.3727 0.5724 0.7366B 0.7044 0.4441 0.2068 0.0610C 0.1159 0.1832 0.2208 0.2024TABLE 3. FUSION RESULTS OF EXAMPLE 3 Fusion algorithm Element ofD1 2m m1 2 3m m m1 2 3 4m m m m1 2 3 4 5m m m m mDST A 0 0 0 0B 0.8571 0.9730 0.9114 0.7461C 0.1429 0.0270 0.0886 0.2539PCR5 A 0.2024 0.1920 0.3413 0.4827B 0.6851 0.7615 0.5116 0.3068C 0.1125 0.0465 0.1471 0.2105New self-adaptive combination rule A 0.1797 0.1246 0.2962 0.4904B 0.7044 0.8467 0.5791 0.3222C 0.1159 0.0287 0.1247 0.1874Table1showsusthat,DSTisverysuitableforfusing bodiesofevidenceinlowdegreeofconflict.However, becausePCR5keepstheconflictingfocalelements,the support degree ofA is just 0.7506 when fusing the fifth body ofevidence.IthasbeenshowninFig.3thatthedegreeofA offeredbyPCR5ismuchlessthanthevalueofferedbyDST (0.9503). When applying the new self-adaptive algorithm, the supportdegreeofAis0.8755,whichachievesagreat improvementforthatofPCR5.Inotherwords,thenew algorithmcanfusethesourcesofevidenceinlowdegreeof conflict well. It can be seen from table 2 that, due to the high degree of conflict, the mass of A in fusion results by applying theDST ruleisalways0.Obviously,itisillogicalinrealworld.By usingthePCR5rule,onecanmaketherightdecision. However,wecanseefromFig.4thatPCR5rulecouldonly offerslowconvergence,whilethenewself-adaptivefusion algorithmnotonlyovercomestheshortageofDSTwhose fusion result is illogical but also makes the right decision with quick convergence. Table3givesthefusionresultsofexample3.Although therearetwobodiesofevidencewhichareinconflictwith otherevidence,ouralgorithmandPCR5willgivetheright results. Besides, it can be seen from Fig.5 that, as the number ofbodiesofevidenceincreases,thenewalgorithmwillgeta better performance on convergence than PCR5.In conclusion, thenewself-adaptivefusionalgorithmisthebestoneamong the three algorithms while dealing with high degree of conflict. Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4236Fig.3. Support degree of A in Example 1 Fig.4. Support degree of A in Example 2 Fig.5. Support degree of A in Example 3 To sum up, the new self-adaptive algorithm can deal with highdegreeofconflictwithagoodperformanceon convergence. V.CONCLUSION BasedonDSTandDSmT,thispaperproposesanew self-adaptivefusionalgorithm.Acontrollingfactoris introducedtoavoidsettingoftheconflictthreshold. Simulationresultsshowthatthenewmodelcanreacha preferablefusionresultnomatterthesourcesofevidenceare inhighdegreeofconflictornot.Furthermore,thenew algorithmoffersaquickconvergenceanditismore appropriate to be used in the real fusion system. REFERENCES [1]LaurenceCholvy.Usinglogictounderstandrelations betweenDSmT andDempster-Shafertheory,ECSQARU2009,LNAI5590,pp.264274, 2009. [2]Yager.OntheDempster-Shaferframeworkandnewcombination rules, Information System, vol. 41, no. 2, pp. 93-137, 1989. [3]MurphyCK.Combiningbelieffunctionswhenevidenceconflicts, Decision Support Systems, vol.29, pp.1-9, 2000. 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